2. A doctor is called to see a sick child. The doctor has prior information that 95% of sick children in that neighborhood have the flu, while the other 05% are sick with measles. Let F stand for an event of a child being sick with flu and M stand for an event of a child being sick with measles. Assume for simplicity that FM=, i.e., that there no other maladies in that neighborhood. A well-known symptom of measles is a rash (the event of having which we denote R). Assume that the probability of having a rash if one has measles is P(RM)=0.95. However, occasionally children with flu also develop rash, and the probability of having a rash if one has flu is P(RF)=0.08. Upon examining the child, the doctor finds a rash. Infer the probability that the child has measles